# Geometry Course Outline

Ηλεκτρονική - Συσκευές

10 Οκτ 2013 (πριν από 4 χρόνια και 9 μήνες)

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Geometry

Key Standards

these comprise a minimum of 70% of Standards Exam

1

Geometry Course Outline

Marking

Period 1

Objectives to Demonstrate Mastery

California Content Standards: Geometry

The teaching of proofs and logical reasoning will be taught
and discussed through out the course.

•Fill in missing statements and reasons

•Construct deductive proofs.

•Construct proofs by contradiction.

G2.0

Students write geometric proofs, including proofs by

•Understand undefined terms: points, lines and planes.

•Define and apply commonly used terms in geometry

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•Use inductive and deductive reasoning.

G1.0

Students demonstrate understanding by identifying
and giving examples of undefined terms, axioms,
theorems, a
nd inductive and deductive reasoning.

•Distinguish between universal and existence statements.

•Construct counterexamples for universal statements.

•Construct counterexamples for existence statements.

G3.0

Students construct and judge the validity of a

logical
argument and give counterexamples to disprove a
statement.

Geometry

Key Standards

these comprise a minimum of 70% of Standards Exam

2

Marking

Period 2

Objectives to Demonstrate Mastery

California Content Standards: Geometry

•Accurately measure an angle, using a protractor.

•Accurately measure a side using a ruler.

•Define and classify polygons according to the number of
sides and angles.

•Define and classify triangles according to the measures of
the sides (equilateral, isosceles and scalene) and measures
of the angles (equiangular, acute, obtuse and right)

•Use mea
sures of sides and/or of interior and exterior
angles of triangles and polygons to solve problems.

G12.0

Students find and use measures of sides and of interior
and exterior angles of triangles and polygons to classify
figures and solve problems.

•Find

the sum of the interior angles, given the number of
sides.

•Find the number of sides, given the sum of the interior
angles.

•Find the sum of the exterior angles, given the number of
sides.

•Find the measure of the exterior angles of a triangle, given
the
interior angles.

•Define regular, concave and convex polygons.

•Use the sum of interior and exterior angles in solving
problems involving polygons.

G13.0

Students prove relationships between angles in
polygons by using properties of complementary,
supple
mentary, vertical, and exterior angles.

•Define parallel and perpendicular lines, planes, and
transversals.

•Find the measure of missing angles, given parallel lines,
intersected by a transversal and the measure of one angle.

•Determine whether lines ar
e parallel given two lines cut by
a transversal and the measure of more than one angle
using corresponding, alternate interior and alternate
exterior angle and sum of same side interior angle
theorems.

•Applying properties of parallel lines, perpendicular
lines,
and diagonals to classify quadrilaterals.

G7.0

Students prove and use theorems involving the
properties of parallel lines
cut by a transversal, the
properties of quadrilaterals, and the properties of
circles.

Geometry

Key Standards

these comprise a minimum of 70% of Standards Exam

3

•Labbel all parts of a circle.

•Define chord, secant, tangent, inscribed angle, inscribed
polygon and circumscribed polygon.

Geometry

Key Standards

these comprise a minimum of 70% of Standards Exam

4

Marking

Period 3

Objectives to Demonstrate Mastery

California Content Standards: Geometry

Use compass and straight edge to do construction such as:

•congruent segme
nts and angles

•segment and perpendicular bisector

•angle bisector

•line parallel to a given line through a point of the line

•line perpendicular to a given point on the line and off the
line.

G 16.0

Students perform basic constructions with a
straighted
ge and compass, such as angle bisectors,
perpendicular bisectors, and the line parallel to a given
line through a point off the line.

•Use the triangle inequality theorem to determine if a trio of
line segments could be the lengths of the sides of a
tri
angle.

•Determine the range of the length of the third side of a
triangle can be, given the lengths of the other two sides.

G6.0

Students know and are able to use the triangle
inequality theorem.

•Define congruent and similar triangles.

•Discover and p
rove basic theorems involving congruence
and similarity.

•Prove two triangles congruent or not, based on given
information.

•Prove two triangles similar or not, based on given
information.

G4.0

Students prove basic theorems involving congruence
and simil
arity.

•Use corresponding parts of congruent triangles to solve
problems.

•Prove two triangles congruent using SAS, ASA, SSS, AAS,
and HL.

•Prove 2 triangles similar using AA, SSS, SAS

•Use properties of proportions to solve problems involving
similar t
riangles.

G 5.0

Students prove that triangles are congruent or similar,
and they are able to use the concept of corresponding
parts of congruent triangles.

Geometry

Key Standards

these comprise a minimum of 70% of Standards Exam

5

Marking

Period 4

Objectives to Demonstrate Mastery

California Content Standards: Geometry

•Cl
assify triangles as acute, obtuse, or right.

•Find the missing side of a right triangle.

•Determine whether the triangle formed is a right triangle
given 3 side lengths

•Solve problems involving the Pythagorean Theorems, ie.
find the diagonals of a room, o
r a rectangle.

•Prove the Pythagorean Theorem.

G15.0

Students use the Pythagorean Theorem to determine
distance and find missing lengths of sides of right
triangles.

G14.0

Students prove the Pythagorean Theorem.

•Learn and use the six basic trigonomet
ric functions.

•Use trigonometric rations to find the missing sides of
triangles when the angles are known.

•Simplify trigonometric expressions using the relationships
between them, ie.
;

G18.0

Students know

the definitions of the basic
trigonometric functions defined by the angles of a right
triangle. They also know and are able to use
elementary relationships between them. ie,

;

•Use trigonometric function
s to find missing sides of right
triangles.

•Find the measure of missing angles of a triangle using
trigonometric functions.

G 19.0 Students use trigonometric functions to solve for an
unknown length of a side of a right triangle, given an
angle and a le
ngth of a side.

•Use the Pythagorean Theorem to find the relationships for
all 30
-
60
-
90 and 45
-
45
-
90 triangles.

•Find the length of all three sides of a 45
-
45
-
90 triangle,
given the length of any one side.

•Find the length of all three sides of a 30
-
60
-
90 triangle
given the length of any one side.

G20.0

Students know and are able to use angle and side
relationships in problems with special right triangles
such as 30
-
60
-
90 and 45
-
45
-
90 triangles.

Geometry

Key Standards

these comprise a minimum of 70% of Standards Exam

6

Marking

Period 5

Objectives to Demonstrate Mastery

Cal
ifornia Content Standards: Geometry

•Know, derive and apply the formulas of perimeter,
circumference and area of common geometric figures,
including circles, rectangles, scalene and equilateral
triangles, rhombi, parallelograms and trapezoids.

•Know, de
rive, and apply the formulas for surface area,
lateral area, and volume of a prism, cylinder, pyramid,
cone and sphere.

G10.0

Students compute areas of polygons, including
rectangles, scalene triangles, equilateral triangles,
rhombi, parallelograms, and

trapezoids.

G8.0

Students know, derive, and solve problems involving
perimeter, circumference, area, volume, lateral area,
and surface area of common geometric figures.

G9.0

Students compute the volumes and surface areas of
prisms, pyramids, cyl
inders, cones, and spheres; and
students commit to memory the formulas for prisms,
pyramids, and cylinders.

•Change one or more dimensions of a polygon and
determine how that change affects the perimeter and area
of the figure.

•Change one or more dimens
ions of a geometric solid and
determine how that change affects the volume of the
figure.

G11.0

Students determine how changes in dimensions affect
the perimeter, area, and volume of common geometric
figures and solids.

Geometry

Key Standards

these comprise a minimum of 70% of Standards Exam

7

Marking

Period 6

Objectives to D
emonstrate Mastery

California Content Standards: Geometry

•Prove the distance formula and the midpoint theorem.

•Determine midpoints and distances in real world
situations.

•Place figures on coordinate axes and label their vertices
and use to prove theor
ems using coordinate geometry.

•Write linear equations in various forms.

•Write equations of circles.

G17.0

Students prove theorems by using coordinate
geometry, including the midpoint of a line segment, the
distance formula and various forms of equation
s of
lines and circles.

•Label all parts of a circle.

•Define chord, secant, tangent, inscribed angle, inscribed
polygon, and circumscribed polygon.

•Using the circle relationships, calculate measures of angles
and segments of tangents, chords, secants
, inscribed
angles, and inscribed and circumscribed polygons.

G21.0

Students prove and solve problems regarding
relationships among chords, secants, tangents,
inscribed angles and inscribed and circumscribed
polygons of circles.

•Identify the transform
ation that has been done to a given
figure.

•Given a figure, be able to perform all of the indicated
transformations on that figure.

G22.0

Students know the effect of rigid motions on figures in
the coordinate plane and space, including rotations,
transl
ations, and reflections.